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Word Problems - PowerPoint

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					Test Topics
 Graph a sinusoid given equation in transformational form or
  functional form
 State mapping rule
 Given the mapping rule, state the transformations
 Given the mapping rule, state equation in functional or
  transformational form
 State transformations
 Given graph state equation as transformation of sine or cosine
 Given word problem graph and state equation
 State amplitude, period, phase shift, principal axis, local maximum,
  local minimum
Transformational                                Functional
  1 ( y VT ) sin 1  x  HT   y VS sin 1  x  HT   VT
                                                               
VS                       HS 
                        
                        
                                           
                                            
                                                        
                                                         HS 
                                                        
                                                                   
                                                                       

1( y 6) sin 2 x 30             y  3sin 2 x 30 6
                                                   
                                                   
                                                   
                                                       
                                                       
                                                               
                                                               
                                                              
3               
                                               
                                                             
                                                                

Transformations                     Rx  No
                                   VT  6
                                   VS  3
                                    HS  1  period 180
                                         2
                                    HT  30
                                    PA y  6
                                                          

Mapping Rule          
                      
                         x, y  1 x 30,3y 6
                             
                             
                             
                                 
                                 
                                 
                                                           
                                                           
                                                           
                            
                                 2
                                 
                                 
                                                           
                                                           
Word Problems
Ferris Wheel


     A Ferris wheel has a diameter of 32 m,
     and its centre is 18 m above the ground.
     The wheel completes one revolution
     every 30 seconds.
a)   Graph a rider’s height above the ground (m) versus
     time (s) during a 2 minute ride. State any assumptions.
b)   Write an equation to model this relationship.
c)   State the domain and range of the function.
Principal Axis



    A Ferris wheel has a diameter of 32 m, and its centre is
    18 m above the ground. The wheel completes one
    revolution every 30 seconds.
Amplitude – Vertical Stretch



    A Ferris wheel has a diameter of 32 m, and its centre is
    18 m above the ground. The wheel completes one
    revolution every 30 seconds.
Period

     A Ferris wheel has a diameter of 32 m, and its centre is
     18 m above the ground. The wheel completes one
     revolution every 30 seconds.
Horizontal Stretch

HS = period
     360             A Ferris wheel has a diameter of 32
                     m, and its centre is 18 m above the
                     ground.

    =   30/360       The wheel completes one
                     revolution every 30 seconds.


    = 1/12
Transformations

Vertical Translation     (Principal Axis)
Vertical Stretch         (Amplitude)
Horizontal Stretch       (Period/360)
Horizontal Translation   (Phase Shift)
Reflection

Write your own equation and graph
Transformations

Vertical Translation     (18)
Vertical Stretch         (16)
Horizontal Stretch       (1/12)
Horizontal Translation   (0)
Reflection               (Yes)
Which equation do you choose?
   1 ( y 16)  sin  1  x
                            
   18                       
                     12     

                                   1 ( y 18)  cos(12 x)
                                   16
 1 ( y 18)  sin(12 x)
16


     1 ( y 18)  sin(12 x)
     16
                                    1 ( y 18)  sin(12 x)
                                    16
Which graph makes sense? Why?


                  1 ( y 18)  cos(12 x)
                  16
Domain=?   Range =?
Domain=?       Range =?

Domain = {x єR, x≥0}

Range = {y єR, 2 ≤ y ≤ 34}
Ocean Cycles
 A point on the ocean rises and falls as waves
  pass. Suppose that a wave passes every 4
  s, and the height of each wave from the crest
  to the trough is 0.5 m.
 Sketch a graph to model the height of the point
  relative to its average height for a complete
  cycle.
 Use exact values to write an equation of the
  form h = a cos kt to model the height of the
  point, h meters, relative to its average
  height, as a function of time, t seconds.
Paddle Steamer

				
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